Neural Network Approach in Forecasting Realized Variance Using High-Frequency Data

Open access


Background: Since high-frequency data have become available, an unbiased volatility estimator, i.e. realized variance (RV) can be computed. Commonly used models for RV forecasting suffer from strong persistence with a high sensitivity to the returns distribution assumption and they use only daily returns. Objectives: The main objective is measurement and forecasting of RV. Two approaches are compared: Heterogeneous AutoRegressive model (HAR-RV) and Feedforward Neural Networks (FNNs). Even though HAR-RV-type models describe RV stylized facts very well, they ignore its nonlinear behaviour. Therefore, FNN-HAR-type models are developed. Methods/Approach: Firstly, an optimal sampling frequency with application to the DAX index is chosen. Secondly, in and out of sample predictions within HAR models and FNNs are compared using RMSE, AIC, the Wald test and the DM test. Weights of FNN-HAR-type models are estimated using the BP algorithm. Results: The optimal sampling frequency of RV is 10 minutes. Within HAR-type models, HAR-RV-J has better, but not significant, forecasting performances, while FNN-HAR-J and FNNLHAR- J have significantly better predictive accuracy in comparison to the FNN-HAR model. Conclusions: Compared to the traditional ones, FNN-HAR-type models are better in capturing nonlinear behaviour of RV. FNN-HAR-type models have better accuracy compared to traditional HAR-type models, but only on the sample data, whereas their out-of-sample predictive accuracy is approximately equal.

1. Adhikari, R., Agrawal, R. K. (2013), “An Introductory Study on Time Series Modeling and Forecasting”, LAP Lambert Academic Publishing, Germany.

2. Aït-Sahalia, Y., Mykland, P. A., Zhang, L. (2005), “How often to sample a continuous-time process in the presence of market microstructure noise”, Review of Financial Studies, Vol. 18, No. 2, pp. 351-416.

3. Aljinović, Z., Poklepović, T. (2013), “Neural networks and vector autoregressive model in forecasting yield curve”, The 6th International Conference on Information Technology (ICIT), Al-Zaytoonah University of Jordan, Amman, Vol. 1, pp. 1-8.

4. Al-Maqaleh, B. M., Al-Mansoub, A. A., Al-Badani, F. N. (2016), “Forecasting using Artificial Neural Network and Statistics Models”, International Journal of Education and Management Engineering, Vol. 6, No. 3, pp. 20-32.

5. Aminian, F., Suarez, E. D., Aminian, M., Walz, D. T. (2006), “Forecasting Economic Data with Neural Networks”, Computational Economics, Vol. 28, No. 1, pp. 71-88.

6. Andersen, T. G., Bollerslev, T., Diebold, F. X. (2007a), “Roughing it up: including jump components in the measurement, modelling and forecasting of return volatility”, The Review of Economics and Statistics, Vol. 89, No. 4, pp. 701-720.

7. Andersen, T. G., Bollerslev, T., Diebold, F. X., Labys, P. (2003), “Modeling and Forecasting Realized Volatility”, Econometrica, Vol. 71, No. 2, pp. 579-625.

8. Andersen, T., Bollerslev, T., Dobrev, D. (2007b), “No-arbitrage semi-martingale restrictions for continuous time volatility models subject to leverage effects, jumps and i.i.d. noise: theory and testable distributional implications”, Journal of Econometrics, Vol. 138, No. 1, pp.125-180.

9. Angus, J. E. (1991), “Criteria For Choosing The Best Neural Network: Part I”, Report No. 91-16.

10. Arnerić, J., Poklepović, T. (2016), “Nonlinear Extension of Asymmetric GARCH Model within Neural Network Framework”, in Zizka, J., Nagamalai, D. (eds.). Computer Science & Information Technology, AIRCC Publishing Corporation, Chennai, India, pp. 101-111.

11. Arnerić, J., Poklepović, T., Aljinović, Z. (2014), “GARCH based artificial neural networks in forecasting conditional variance of stock returns”, Croatian Operational Research Review, Vol. 5, No. 2, pp. 329-343.

12. Bandi, F. M., Russell, J. R. (2008), “Microstructure Noise, Realized Variance, and Optimal Sampling”, The Review of Economic Studies, Vol. 75, No. 1, pp. 339-369.

13. Bandi, F. M., Russell, J. R. (2011), “Market Microstructure Noise, Integrated Variance Estimators, and the Accuracy of Asymptotic Approximations”, Journal of Econometrics, Vol. 160, No. 1, pp. 145-159.

14. Barndorff-Nielsen, O. E., Shephard, N. (2002a), “Econometric Analysis of Realised Volatility and its use in Estimating Stochastic Volatility Models”, Journal of the Royal Statistical Society, Vol. 64, No. 2, pp. 253-280.

15. Barndorff-Nielsen, O. E., Shephard, N. (2002b), “Estimating Quadratic Variation Using Realized Variance”, Journal of Applied Econometrics, Vol. 17, No. 5, pp. 457-478.

16. Barndorff-Nielsen, O. E., Shephard, N. (2004), “Econometric analysis of realised covariation: high frequency covariance, regression and correlation in financial economics”, Econometrica, Vol. 72, No. 3, pp. 885-925.

17. Baruník, J., Křehlík, T. (2016), “Combining high frequency data with non-linear models for forecasting energy market volatility”, Expert Systems With Applications, Vol. 55, pp. 222-242.

18. Bektipratiwi, A., Irawan, M. I. (2011), “A RBF-EGARCH neural network model for time series forecasting”, Proceedings of The IceMATH 2011, pp. 1-8.

19. Bildirici, M., Ersin, Ö. Ö. (2009), “Improving forecasts of GARCH family models with the artificial neural networks: An application to the daily returns in Istanbul Stock Exchange”, Expert Systems with Applications, Vol. 36, No. 4, pp. 7355-7362.

20. Bildirici, M., Ersin, Ö. Ö. (2012), “Nonlinear volatility models in economics: smooth transition and neural network augmented GARCH, APGARCH, FIGARCH and FIAPGARCH models”, MPRA Paper No. 40330.

21. Bildirici, M., Ersin, Ö. Ö. (2014), “Modelling Markov Switching ARMA-GARCH Neural Networks Models and an Application to Forecasting Stock Returns”, Hindawi Publishing Corporation: The Scientific World Journal, Article ID 497941, pp. 1-21.

22. Binner, J. M., Elger, C. T., Nilsson, B., Tepper, J. A. (2006), “Predictable non-linearities in U.S. inflation”, Economics Letters, Vol. 93, No. 3, pp. 323-328.

23. Bollerslev, T. (1986), “Generalized autoregressive Conditional Heteroskedasticity”, Journal of Econometrics, Vol. 31, No. 3, pp. 307-327.

24. Buse, A. (1982), “The Likelihood Ratio, Wald, and Lagrange Multiplier Tests: An Expository Note”, The American Statistician, Vol. 36, No. 3, pp. 153-157.

25. Chaudhuri, T. D, Ghosh, I. (2016), „Artificial Neural Network and Time Series Modeling Based Approach to Forecasting the Exchange Rate in a Multivariate Framework“, Journal of Insurance and Financial Management, Vol. 1, No. 5, pp. 92-123.

26. Choudhary, A., Haider, A. (2008), “Neural network models for inflation forecasting: an appraisal”, Discussion Papers in Economics, University of Surrey, UK, DP 08/08.

27. Clements, A. E., Liao, Y. (2013), “Modeling and forecasting realized volatility: getting the most out of the jump component”, NCER Working Paper Series, Working Paper #93, August.

28. Corsi, F. (2003), “A Simple Long Memory Model of Realized Volatility”, manuscript, University of Southern Switzerland.

29. Corsi, F. (2009), “A simple approximate long memory model of realized volatility”, Journal of Financial Econometrics, Vol. 7, No. 2, pp. 174-196.

30. Corsi, F., Audrino, F., Reno, R. (2012), “HAR Modeling for Realized Volatility Forecasting”, in Handbook of Volatility Models and Their Applications, John Wiley & Sons, New Jersey, USA, pp. 363-382.

31. Dedi, R., Yoga, A. N., Rahmawati, K. D. (2011), ”Forecasting the Indonesian Government Securities Yield Curve Using Neural Networks and Vector Autoregressive Model“, ISI 58th Session, Dublin, August 21-26, 2011.

32. Degiannakis, S., Floros, C. (2015), “Modelling and Forecasting High Frequency Financial Data”, Palgrave Macmillan.

33. Diebold, F. X., Mariano, R. S. (1995), “Comparing Predictive Accuracy”, Journal of Business and Economic Statistics, Vol. 13, No. 3, pp. 253-263.

34. Doukim, C. A., Dargham, J. A., Chekima, A. (2010), “Finding the number of hidden neurons for an MLP neural network using coarse to fine search technique”, in Proceedings of the 10th International Conference on Information Sciences, Signal Processing and Their Applications (ISSPA '10), May, pp. 606-609.

35. Engle, R. F. (1982), “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation”, Econometrica, Vol. 50, No. 4, pp. 987-1007.

36. Franses, P. H., van Dijk, D. (2003), “Nonlinear Time Series Models in Empirical Finance”, Cambridge University Press.

37. Gonzales, S. (2000), “Neural Networks for Macroeconomic Forecasting: A Complementary Approach to Linear Regression Models”, Working Paper 2000-07.

38. Hagiwara, M. (1994), “A simple and effective method for removal of hidden units and weights”, Neurocomputing, Vol. 6, No. 2, pp. 207-218.

39. Hansen, P. R., Lunde, A. (2005), “A realized variance for the whole day based on intermittent high-frequency data”, Journal of Financial Econometrics, Vol. 3, No. 4, pp. 525-554.

40. Hansen, P. R., Lunde, A. (2006), “Realized variance and market microstructure noise”, Journal of Business and Economic Statistics, Vol. 24, No. 2, pp. 127-161.

41. Huang, C., Gong, X., Chen, X., Wen, F. (2013), “Measuring and Forecasting Volatility in Chinese Stock Market Using HAR-CJ-M Model”, Research Article, Hindawi Publishing Corporation Abstract and Applied Analysis, Article ID 143194, pp. 1-13.

42. Junior, M. V. W., Pereira, P. L. V. (2011), “Modeling and Forecasting Realized Volatility: Evidence from Brazil”, Brazilian Review of Econometrics, Vol. 31, No. 2, pp. 315-337

43. Jurkovič, J. (2013), “Forecasting Realized Volatility Using Neural Networks”, Master thesis, Charles University in Prague Faculty of Social Sciences

44. Kaashoek, J. F., van Dijk, H. K. (2001), “Neural networks as econometric tool”, Econometric Institute Report, EI 2001-05, pp. 1-32.

45. Keeni, K., Nakayama, K., Shimodaira, H. (1999), “Estimation of initial weights and hidden units for fast learning of multi-layer neural networks for pattern classification”, in Proceedings of the International Joint Conference on Neural Networks (IJCNN '99), Vol. 3, IEEE, July, pp. 1652-1656.

46. Li, J. Y., Chow, T. W. S., Yu, Y. L. (1995), “Estimation theory and optimization algorithm for the number of hidden units in the higher-order feedforward neural network”, in Proceedings of the IEEE International Conference on Neural Networks, Vol. 3, December, pp. 1229-1233.

47. Mantri, J. K., Gahan, P., Nayak, B. B. (2010), “Artificial Neural Networks - An Application to Stock Market Volatility”, International Journal of Engineering Science and Technology, Vol. 2, No. 5, pp. 1451-1460.

48. Mantri, J. K., Mohanty, D., Nayak, B.B. (2012), “Design Neural Network for Stock Market Volatility: Accuracy Measurement”, International Journal on Computer Technology and Applications, Vol. 3, No. 1, pp. 242-250.

49. Medeiros, M. C., Teräsvirta, T., Rech, G. (2006), “Building Neural Network Models for Time Series: A Statistical Approach”, Journal od Forecasting, No. 25, No. 1, pp. 49-75.

50. Moshiri, S., Cameron, N. (2000), “Neural Networks Versus Econometric Models in Forecasting Inflation”, Journal of Forecasting, Vol. 19, No. 3, pp. 201-217.

51. Rosa, R., Maciel, L., Gomide, F., Ballini, R. (2014), “Evolving Hybrid Neural Fuzzy Network for Realized Volatility Forecasting with Jumps”, IEEE Conference on Computational Intelligence for Financial Engineering & Economics (CIFEr), London, pp. 481-488.

52. Teräsvirta, T., Tjøstheim, D., Granger, C. W. J. (2008), “Modelling nonlinear economic time series”, Oxford University Press, New York,.

53. Teräsvirta, T., van Dijk, D., Medeiros, M. C. (2005), “Linear models, smooth transition autoregressions, and neural networks for forecasting macroeconomic time series: A reexamination”, International Journal of Forecasting, Vol. 21, No. 4, pp. 755-774.

54. Wang, J., Wang, J., Fang, W., Niu, H. (2016), “Financial Time Series Prediction Using Elman Recurrent Random Neural Networks“, Hindawi Publishing Corporation Computational Intelligence and Neuroscience, Article ID 4742515, pp. 1-14.

55. Zapranis, A., Refenes, A.-P. (1999), “Neural model identification, variable selection and model adequacy”, Journal of Forecasting, Vol. 18, No. 5, pp. 299-332.

56. Zekić-Sušac, M., Kliček, B. (2002), “A Nonlinear Strategy of Selecting NN Architectures for Stock Return Predictions”, Finance, Proceedings from the 50th Anniversary Financial Conference Svishtov, Bulgaria, 11-12 April, Svishtov, Veliko Tarnovo, ABAGAR, pp. 325-355.

57. Zhang, G. P. (2003), “Time series forecasting using hybrid ARIMA and neural network model”, Neurocomputing, Vol. 50, pp. 159-175.

58. Zhang, J., Morris, A. J. (1998), “A sequential learning approach for single hidden layer neural networks”, Neural Networks, Vol. 11, No. 1, pp. 65-80.

59. Zhang, L., Aït-Sahalia, Y., Mykland, P. A. (2005), “A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High-Frequency Data”, Journal of the American Statistical Association, Vol. 100, No. 472, pp. 1394-1411.

Business Systems Research Journal

The Journal of Society for Advancing Innovation and Research in Economy

Journal Information


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 162 162 20
PDF Downloads 142 142 16